Select each pair of expressions that are equivalent. 1. 3x + 14 – x + 112 and 4x + 134
2. 2 + 6x and 2(3x + 1)
3. 3(x + 1) – (1 – x) and 2x + 3
4. 3x and 4(x + 1) – x – 4
5. 5.5 + 2.2x + 3.8x – 4.1 and 1.4 + 6x

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0